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Spotlight on Optics

March 2011

Spotlight Summary by Thomas Udem

Over the past decade the progress on optical atomic clocks, which use very rapid oscillations of light, has been tremendous. Such clocks are capable of measuring time intervals with a much finer ruler than conventional Cs atomic clocks that operate at 9.2 GHz. The optical frequency combs introduced in the late 1990s have provided a suitable optical clockwork mechanism that can readily count these oscillations for time keeping. Several optical transitions in atoms and ions have been under investigation for that purpose. As an important property of these transitions one would require them to be as insensitive as possible to external frequency shifting perturbations, which, as a whole, are hard to avoid. Single trapped ions are currently most advanced in this respect, because it is much easier to isolate them from the rest of the world. Current ion trap setups can store only a few ions, and in practice only one of them at a place that is free of the frequency shifting influences of the trapping fields. For that reason the error signal used to steer the laser onto the ions resonance is weak and needs to be averaged for a long time. This is where the optical reference cavities kick in.

In an optical clock the laser that is used for interrogating the ion is stabilized to a high-finesse cavity to bridge the time between the quantum jumps. Typically, the jump rate is of the order of seconds for the best optical clocks. A rather long lifetime, i.e., narrow transition linewidth, is needed to correct the laser frequency with high fidelity.

Picking the best transition for that purpose does not depend only on its sensitivity to the outside world but also on the stability of the available reference cavity: If the unpredictable part of its drift is too large between quantum jumps, one better resort to a larger transition rate, i.e., to a larger line width and vice versa. So the minimum useful transition linewidth depends on the performance of the reference cavity. With a more stable cavity a narrower transition may be used.

To be compatible with a ~1 Hz transition width at a transition frequency of ~1015 Hz, the length of a suitable reference cavity has to be stable within the same fraction. In absolute units this typically means something on the order of ~10-16 m, or about a tenth the size of a proton. Of course, the mirror roughness is much larger than this, but the standing wave inside the cavity is averaging over many atoms of the mirror surface. Thermal expansion is compensated by employing a material with a vanishing linear coefficient of thermal expansion. In addition, temperature is stabilized to compensate the quadratic dependence. Acceleration due to seismic noise imposes forces on the cavity that in turn deforms it. To compensate for this, cavities are often installed on several layers of vibration isolation platforms. For the past few years, the new trick is to orient and form the cavity spacer such that accelerations deform all but the critical length that sets its resonance frequency. Now the state of the art is limited by the thermal vibrations of the atoms that make up the spacer and the mirrors, even though a large number of them enter with a very well defined average position.

A serious limitation of the optical clocks is their complexity and size. So far they cannot be transported and compared as has been done with the Cs clocks. Frequency combs and interrogation lasers contribute significantly but have been reduced in size considerably. A major step to make a transportable, high-performance reference cavity has now been presented by Leibrandt and co-workers, one of whom is Jim Bergquist, a leader in the field for decades. They introduced a spherical cavity spacer that is, owing to its symmetric shape, intrinsically insensitive to accelerations in all directions. The spacer possesses a bore hole on a diameter with the optical axis. The mirrors are attached to the surface of the sphere and are held by a tweezers-like structure that compresses the sphere on another diameter that is the support axis. If the latter is parallel to the optical axis, the cavity length is reduced by application of a force, while this length is extended if the support axis is at 90º to the optical axis as a result of sphere being squeezed. So there is an angle between the two axes such that the “tweezers" force leaves the length of the optical axis unaffected. The resonance frequency does not depend on the applied force, i.e. it is squeeze insensitive. With that, the resonance frequency of the reference cavity becomes independent of the thermal expansions and thermal noise of its support. The spherical shape also makes it insensitive to changes in orientation, so that no tedious alignment procedures are required after transport. Together with the compactness of the design, this is certainly another step toward a compact transportable optical atomic clock.